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R. Barrett and P. P. Delsanto
booby prize. He then offers the contestants a choice of staying with their original
selection, or changing their mind and selecting the other remaining closed door.
What should they do?
The intuitive, or common sense, answer is that it doesn’t matter, as there are
now only two closed doors, and surely there is an equal likelihood of finding
the car lying behind each of them. This answer is wrong. Contestants will
have twice as much chance of winning the car if they change their selection
from their original choice to the other door.
The solution of the Monty Hall problem is discussed in Appendix 5.5.
However, the point we wish to make here is that as soon as the host opens
the door revealing the booby prize, the probability distribution associated
with the car’s location is changed. Originally there was an equal probability
of the car being located behind each of the three doors. Now we know for
certain that it is not behind the door that was opened. We have received
extra information that changes the probability distribution of the car at this
moment. Information is an important concept in QM, but one which we
cannot pursue further here.
5.7 Wheeler’s Delayed Choice Experiment
Let us continue with our thought experiments by envisioning two narrow
slits close together and allowing a plane wave (in the wave representation),
or a stream of particles (in the corpuscular representation), to be incident
upon them. The setup is sketched in Fig. 5.4. We will discuss the case of
light waves (i.e. photons), but we could just as well have used electrons, or
any other quantum particles.
From what we have already discussed, we would expect the waves passing
through the two slits to interfere, and produce an interference pattern of light
and dark fringes on the optical screen placed behind the slits similar to that
shown in Fig. 5.5.
Naïvely, we may tell ourselves that one photon has passed through one slit,
a second through the other slit, and their wave functions have interfered with
each other to produce the above interference pattern. However, it is not quite
so simple, and QM has a few more tricks to play.
Let us continue our thought experiment by reducing the intensity of the
incident beam so that only one photon (or electron, if we wish) is in flight
at any time. In other words, we wait until one photon has collided with our
photographic plate, before releasing the next one on its journey. When the
photon that is underway reaches the slits, it should pass through one or the
R. Barrett and P. P. Delsanto
booby prize. He then offers the contestants a choice of staying with their original
selection, or changing their mind and selecting the other remaining closed door.
What should they do?
The intuitive, or common sense, answer is that it doesn’t matter, as there are
now only two closed doors, and surely there is an equal likelihood of finding
the car lying behind each of them. This answer is wrong. Contestants will
have twice as much chance of winning the car if they change their selection
from their original choice to the other door.
The solution of the Monty Hall problem is discussed in Appendix 5.5.
However, the point we wish to make here is that as soon as the host opens
the door revealing the booby prize, the probability distribution associated
with the car’s location is changed. Originally there was an equal probability
of the car being located behind each of the three doors. Now we know for
certain that it is not behind the door that was opened. We have received
extra information that changes the probability distribution of the car at this
moment. Information is an important concept in QM, but one which we
cannot pursue further here.
5.7 Wheeler’s Delayed Choice Experiment
Let us continue with our thought experiments by envisioning two narrow
slits close together and allowing a plane wave (in the wave representation),
or a stream of particles (in the corpuscular representation), to be incident
upon them. The setup is sketched in Fig. 5.4. We will discuss the case of
light waves (i.e. photons), but we could just as well have used electrons, or
any other quantum particles.
From what we have already discussed, we would expect the waves passing
through the two slits to interfere, and produce an interference pattern of light
and dark fringes on the optical screen placed behind the slits similar to that
shown in Fig. 5.5.
Naïvely, we may tell ourselves that one photon has passed through one slit,
a second through the other slit, and their wave functions have interfered with
each other to produce the above interference pattern. However, it is not quite
so simple, and QM has a few more tricks to play.
Let us continue our thought experiment by reducing the intensity of the
incident beam so that only one photon (or electron, if we wish) is in flight
at any time. In other words, we wait until one photon has collided with our
photographic plate, before releasing the next one on its journey. When the
photon that is underway reaches the slits, it should pass through one or the